Question

If $- \frac{3}{2}$then $\frac{3}{2}$ is equal to.

• A. $z^{'}$
• B. $z.z' = z$
• C. $z' =$
• D. None of these

Answer 1

Answer: (B)

$z.z' = z$

Answer 2

If $2x + 3y = 4$

$- 3x + 2y = 1$

$x = \frac{5}{13},y = \frac{14}{13}$

⇒ $x + iy = \frac{4 + i}{2 - 3i} = \frac{(4 + i)(2 + 3i)}{13} = \frac{5}{13} + \frac{14}{13}i$

∴ $(x^{4} + 2xi) - (3x^{2} + yi) = (3 - 5i) + (1 + 2yi)$

$\Rightarrow (x^{4} - 3x^{2}) + i(2x - 3y) = 4 - 5i$

$x^{4} - 3x^{2} = 4$

Trick : $2x - 3y = - 5$

Let $x = \pm 2$, then $y = 3,\frac{1}{3}$i.e., $x = 2,y = 3$.

Now put $x = - 2,$ then $y = \frac{1}{3}$.

Also option (2) gives 4(1) – 3=1.